A008892 Aliquot sequence starting at 276.

276, 396, 696, 1104, 1872, 3770, 3790, 3050, 2716, 2772, 5964, 10164, 19628, 19684, 22876, 26404, 30044, 33796, 38780, 54628, 54684, 111300, 263676, 465668, 465724, 465780, 1026060, 2325540, 5335260, 11738916, 23117724, 45956820, 121129260, 266485716

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

It is an open question whether this sequence ever reaches 0. The trajectory has been calculated to 2145 terms, and is still growing, term 2145 being a 214-digit number (see FactorDB link). - N. J. A. Sloane, Jan 11 2023

The aliquot sequence starting at 306 joins this sequence after one step.

This sequence cannot be extended backwards, since A359132(276) = -1. - N. J. A. Sloane, Jan 10 2023

One can note that the k-tuple abundance of 276 is only 5, since a(6) = 3790 is deficient. On the other hand, the k-tuple abundance of a(8) = 2716 is 164 since a(172) is deficient (see A081705 for definition of k-tuple abundance). - Michel Marcus, Dec 31 2013

References

• K. Chum, R. K. Guy, M. J. Jacobson, Jr., and A. S. Mosunov, Numerical and statistical analysis of aliquot sequences. Exper. Math. 29 (2020), no. 4, 414-425; arXiv:2110.14136, Oct. 2021 [math.NT].
• Richard K. Guy, Unsolved Problems in Number Theory, B6.
• Richard K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.

Links

• Tyler Busby, Table of n, a(n) for n = 0..2157 (terms 0..2127 from Daniel Suteu, terms 2128..2140 from Jeppe Stig Nielsen)
• Christophe Clavier, Aliquot Sequences
• Christophe Clavier, Trajectory of 276 - the first 1576 terms and their factorizations
• Christophe Clavier, Trajectory of 276 - the first 1576 terms and their factorizations [Cached copy]
• Wolfgang Creyaufmüller, Lehmer Five
• Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
• Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
• FactorDB (factordb.com), Search result for last 20 terms of 276 sequence.
• Brady Haran and Ben Sparks, An amazing thing about 276, Numberphile YouTube video, 2024.
• N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 13.
• Paul Zimmermann, Recent information
• Index entries for sequences related to aliquot parts.

Crossrefs

Cf. A001065, A098007 (length of aliquot sequences).

Cf. A008885 (aliquot sequence starting at 30), ..., A008891 (starting at 180).

Programs

Maple

f := proc(n) option remember; if n = 0 then 276; else sigma(f(n-1))-f(n-1); fi; end:

Mathematica

NestList[DivisorSigma[1, #] - # &, 276, 50] (* Alonso del Arte, Feb 24 2018 *)

PARI

a(n, a=276)={for(i=1,n,a=sigma(a)-a);a} \\ M. F. Hasler, Feb 24 2018

Formula

a(n+1) = A001065(a(n)). - R. J. Mathar, Oct 11 2017